Statistics (Faculty of Science)
Statistics is motivated by the need to extract information from data, to quantify uncertainty, and to make predictions about random phenomena. To do this effectively, sophisticated mathematical and probabilistic techniques and computational tools are needed. Core areas of expertise include Bayesian inference, biostatistics, computational statistics, highdimensional data modeling, multivariate analysis, and survival analysis.
DETAILED PROGRAM OUTLINES:
Program Requirement:
The Minor may be taken in conjunction with any primary program in the Faculty of Science. Students should declare their intention to follow the Minor Statistics at the beginning of the penultimate year and must obtain approval for the selection of courses to fulfil the requirements for the Minor from the Departmental Chief Adviser (or delegate).
All courses counted towards the Minor must be passed with a grade of C or better. Generally, no more than 6 credits of overlap are permitted between the Minor and the primary program. However, with an approved choice of substantial courses, the overlap restriction may be relaxed to 9 credits for students whose primary program requires 60 credits or more, and to 12 credits when the primary program requires 72 credits or more.
Required Courses (15 credits)
* MATH 223 may be replaced by MATH 235 and MATH 236. In this case the complementary credit requirement is reduced by 3 credits.

MATH 222 Calculus 3 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Taylor series, Taylor's theorem in one and several variables. Review of vector geometry. Partial differentiation, directional derivative. Extreme of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133
 Restriction: Not open to students who have taken CEGEP course 201303 or MATH 150, MATH 151 or MATH 227
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Jeremy D Macdonald
 Jérôme Fortier

MATH 223 Linear Algebra 3 Credits*
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Review of matrix algebra, determinants and systems of linear equations. Vector spaces, linear operators and their matrix representations, orthogonality. Eigenvalues and eigenvectors, diagonalization of Hermitian matrices. Applications.
Offered by: Mathematics and Statistics
 Fall and Winter
 Prerequisite: MATH 133 or equivalent
 Restriction: Not open to students in Mathematics programs nor to students who have taken or are taking MATH 236, MATH 247 or MATH 251. It is open to students in Faculty Programs
 Symbols:
 *
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Djivede A Kelome
 Jeremy D Macdonald

MATH 323 Probability 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 141 or equivalent.
 Restriction: Intended for students in Science, Engineering and related disciplines, who have had differential and integral calculus
 Restriction: Not open to students who have taken or are taking MATH 356
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Jose Andres Correa
 David B Wolfson, Djivede A Kelome

MATH 324 Statistics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Offered by: Mathematics and Statistics
 Fall and Winter
 Prerequisite: MATH 323 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 357
 You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Masoud AsgharianDastenaei

MATH 423 Regression&Anal of Variance 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Leastsquares estimators and their properties. Analysis of variance. Linear models with general covariance. Multivariate normal and chisquared distributions; quadratic forms. General linear hypothesis: Ftest and ttest. Prediction and confidence intervals. Transformations and residual plot. Balanced designs.
Offered by: Mathematics and Statistics
 Fall
 Prerequisites: MATH 324, and MATH 223 or MATH 236
 Restriction: Not open to students who have taken or are taking MATH 533.
 Symbols:
 Terms
 Fall 2019
 Instructors
 Yi Yang
Complementary Courses (9 credits)
9 credits selected from:

CHEM 593 Statistical Mechanics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Chemistry: Intermediate topics in statistical mechanics, including: modern and classical theories of real gases and liquids, critical phenomena and the renormalization group, timedependent phenomena, linear response and fluctuations, inelastic scattering, Monte Carlo and molecular dynamics methods.
Offered by: Chemistry
 Symbols:
 Terms
 Fall 2019
 Instructors
 David M Ronis

GEOG 351 Quantitative Methods 3 Credits
 Fall
 Winter
 Summer
Offered in the:Geography: Multiple regression and correlation, logit models, discrete choice models, gravity models, facility location algorithms, survey design, population projection.
Offered by: Geography
 Winter
 3 hours
 Prerequisite: GEOG 202 or permission of instructor
 You may not be able to get credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.
 Symbols:
 Terms
 Winter 2020
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 208 Intro to Statistical Computing 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Basic data management. Data visualization. Exploratory data analysis and descriptive statictics. Writing functions. Simulation and parallel computing. Communication data and documenting code for reproducible research.
Offered by: Mathematics and Statistics
 Prerequisite(s): MATH 133
 Symbols:
 Terms
 Fall 2019
 Instructors
 Russell Steele

MATH 427 Statistical Quality Control 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Introduction to quality management; variability and productivity. Quality measurement: capability analysis, gauge capability studies. Process control: control charts for variables and attributes. Process improvement: factorial designs, fractional replications, response surface methodology, Taguchi methods. Acceptance sampling: operating characteristic curves; single, multiple and sequential acceptance sampling plans for variables and attributes.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 Fall 2019
 Instructors
 Christian Genest

MATH 447 Intro. to Stochastic Processes 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains, transition matrices, classification of states, ergodic theorem, examples. Birth and death processes, queueing theory.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 323
 Restriction: Not open to students who have taken or are taking MATH 547.
 Symbols:
 Terms
 Winter 2020
 Instructors
 Russell Steele

MATH 523 Generalized Linear Models 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Modern discrete data analysis. Exponential families, orthogonality, link functions. Inference and model selection using analysis of deviance. Shrinkage (Bayesian, frequentist viewpoints). Smoothing. Residuals. Quasilikelihood. Contingency tables: logistic regression, loglinear models. Censored data. Applications to current problems in medicine, biological and physical sciences. R software.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 Winter 2020
 Instructors
 Johanna Neslehova

MATH 525 Sampling Theory & Applications 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Simple random sampling, domains, ratio and regression estimators, superpopulation models, stratified sampling, optimal stratification, cluster sampling, sampling with unequal probabilities, multistage sampling, complex surveys, nonresponse.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 545 Intro to Time Series Analysis 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Stationary processes; estimation and forecasting of ARMA models; nonstationary and seasonal models; statespace models; financial time series models; multivariate time series models; introduction to spectral analysis; long memory models.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 Winter 2020
 Instructors
 Russell Steele

MATH 556 Mathematical Statistics 1 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Distribution theory, stochastic models and multivariate transformations. Families of distributions including locationscale families, exponential families, convolution families, exponential dispersion models and hierarchical models. Concentration inequalities. Characteristic functions. Convergence in probability, almost surely, in Lp and in distribution. Laws of large numbers and Central Limit Theorem. Stochastic simulation.
Offered by: Mathematics and Statistics
 Fall
 Prerequisite: MATH 357 or equivalent
 Symbols:
 Terms
 Fall 2019
 Instructors
 David A Stephens

MATH 557 Mathematical Statistics 2 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Sampling theory (including largesample theory). Likelihood functions and information matrices. Hypothesis testing, estimation theory. Regression and correlation theory.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 556
 Symbols:
 Terms
 Winter 2020
 Instructors
 Masoud AsgharianDastenaei

PHYS 362 Statistical Mechanics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: Quantum states and ensemble averages. FermiDirac, BoseEinstein and Boltzmann distribution functions and their applications.
Offered by: Physics
 Winter
 3 hours lectures
 Prerequisites: MATH 248 or equivalents, PHYS 253.
 Restriction: Honours students, or permission of the instructor
 Restriction: Not open to students taking or having passed PHYS 333
 Symbols:
 Terms
 Winter 2020
 Instructors
 Martin Grant

PHYS 559 Advanced Statistical Mechanics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Physics: Scattering and structure factors. Review of thermodynamics and statistical mechanics; correlation functions (static); mean field theory; critical phenomena; broken symmetry; fluctuations, roughening.
Offered by: Physics
 Fall
 3 hours lectures
 Restriction: U3 Honours students, graduate students, or permission of the instructor
 Symbols:
 Terms
 Fall 2019
 Instructors
 William Coish

SOCI 504 Quantitative Methods 1 3 Credits
 Fall
 Winter
 Summer
Offered in the:Sociology (Arts): An introduction to basic regression techniques commonly used in the social sciences. Covers the least squares linear regression model in depth and may introduce models for discrete dependent variables as well as the maximumlikelihood approach to statistical inference. Emphasis on the assumptions behind regression models and correct interpretation of results. Assignments will emphasize practical aspects of quantitative analysis.
Offered by: Sociology
 Symbols:
 Terms
 Fall 2019
 Instructors
 Thomas G Soehl
No more than 6 credits may be taken outside the Department of Mathematics and Statistics.
Further credits (if needed) may be freely chosen from the required and complementary courses for majors and honours students in Mathematics, with the obvious exception of courses that involve duplication of material.
Program Requirement:
(45 or 48 credits)
This program provides training in statistics, with a solid mathematical core, and basic training in computing. With strong performance in an appropriate selection of courses, this program can lead to "A.Stat." professional accreditation from the Statistical Society of Canada, which is regarded as the entry level requirement for Statisticians practising in Canada.
Students may complete this program with a minimum of 45 credits or a maximum of 48 credits depending on whether or not they are required to take MATH 203.
Program Prerequisites
Students entering the Core Science Component in Statistics are normally expected to have completed the courses below or their equivalents. Otherwise they will be required to make up any deficiencies in these courses over and above the 45 credits required for the program.

MATH 133 Linear Algebra and Geometry 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Systems of linear equations, matrices, inverses, determinants; geometric vectors in three dimensions, dot product, cross product, lines and planes; introduction to vector spaces, linear dependence and independence, bases; quadratic loci in two and three dimensions.
Offered by: Mathematics and Statistics
 3 hours lecture, 1 hour tutorial
 Prerequisite: a course in functions
 Restriction A: Not open to students who have taken MATH 221 or CEGEP objective 00UQ or equivalent.
 Restriction B: Not open to students who have taken or are taking MATH 123, MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.
 Restriction C: Not open to students who are taking or have taken MATH 134.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Rosalie BélangerRioux

MATH 140 Calculus 1 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Review of functions and graphs. Limits, continuity, derivative. Differentiation of elementary functions. Antidifferentiation. Applications.
Offered by: Mathematics and Statistics
 3 hours lecture, 1 hour tutorial
 Prerequisite: High School Calculus
 Restriction: Not open to students who have taken MATH 120, MATH 139 or CEGEP objective 00UN or equivalent
 Restriction: Not open to students who have taken or are taking MATH 122 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics
 Each Tutorial section is enrolment limited
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Sidney Trudeau
 Jérôme Fortier

MATH 141 Calculus 2 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): The definite integral. Techniques of integration. Applications. Introduction to sequences and series.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 139 or MATH 140 or MATH 150.
 Restriction: Not open to students who have taken MATH 121 or CEGEP objective 00UP or equivalent
 Restriction Note B: Not open to students who have taken or are taking MATH 122 or MATH 130 or MATH 131, except by permission of the Department of Mathematics and Statistics.
 Each Tutorial section is enrolment limited
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Jeremy D Macdonald, Sidney Trudeau
In addition, a student who has not completed the equivalent of MATH 203 on entering the program must consult an academic adviser and take MATH 203 in the first semester, increasing the total number of program credits from 45 to 48.
Required Courses (27 credits)
* Students who have successfully completed a course equivalent to MATH 222 with a grade of C or better may omit MATH 222, but must replace it with 3 credits of complementary courses.
** Students who have sufficient knowledge in a programming language do not need to take COMP 202, but must replace it by either COMP 250 or COMP 350.
***MATH 236 is an equivalent prerequisiste to MATH 223 for required and complementary Computer Science courses listed below.
+ Students have to take MATH 204 prior to MATH 324.

COMP 202 Foundations of Programming 3 Credits**
 Fall
 Winter
 Summer
Offered in the:Computer Science (Sci): Introduction to computer programming in a high level language: variables, expressions, primitive types, methods, conditionals, loops. Introduction to algorithms, data structures (arrays, strings), modular software design, libraries, file input/output, debugging, exception handling. Selected topics.
Offered by: Computer Science
 3 hours
 Prerequisite: a CEGEP level mathematics course
 Restrictions: COMP 202 and COMP 208 cannot both be taken for credit. COMP 202 is intended as a general introductory course, while COMP 208 is intended for students interested in scientific computation. COMP 202 cannot be taken for credit with or after COMP 250
 Symbols:
 **
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Giulia Alberini, Elizabeth Patitsas
 Giulia Alberini

MATH 204 Principles of Statistics 2 3 Credits+
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): The concept of degrees of freedom and the analysis of variability. Planning of experiments. Experimental designs. Polynomial and multiple regressions. Statistical computer packages (no previous computing experience is needed). General statistical procedures requiring few assumptions about the probability model.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 203 or equivalent. No calculus prerequisites
 Restriction: This course is intended for students in all disciplines. For extensive course restrictions covering statistics courses see Section 3.6.1 of the Arts and of the Science sections of the calendar regarding course overlaps.
 You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.
 Symbols:
 +
 Terms
 Winter 2020
 Instructors
 Christian Genest

MATH 222 Calculus 3 3 Credits*
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Taylor series, Taylor's theorem in one and several variables. Review of vector geometry. Partial differentiation, directional derivative. Extreme of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 141. Familiarity with vector geometry or Corequisite: MATH 133
 Restriction: Not open to students who have taken CEGEP course 201303 or MATH 150, MATH 151 or MATH 227
 Symbols:
 *
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Jeremy D Macdonald
 Jérôme Fortier

MATH 235 Algebra 1 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Sets, functions and relations. Methods of proof. Complex numbers. Divisibility theory for integers and modular arithmetic. Divisibility theory for polynomials. Rings, ideals and quotient rings. Fields and construction of fields from polynomial rings. Groups, subgroups and cosets; group actions on sets.
Offered by: Mathematics and Statistics
 Fall
 3 hours lecture; 1 hour tutorial
 Prerequisite: MATH 133 or equivalent
 Symbols:
 Terms
 Fall 2019
 Instructors
 Daniel T Wise

MATH 236 Algebra 2 3 Credits***
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Linear equations over a field. Introduction to vector spaces. Linear mappings. Matrix representation of linear mappings. Determinants. Eigenvectors and eigenvalues. Diagonalizable operators. CayleyHamilton theorem. Bilinear and quadratic forms. Inner product spaces, orthogonal diagonalization of symmetric matrices. Canonical forms.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 235
 Symbols:
 ***
 Terms
 Winter 2020
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 242 Analysis 1 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): A rigorous presentation of sequences and of real numbers and basic properties of continuous and differentiable functions on the real line.
Offered by: Mathematics and Statistics
 Fall
 Prerequisite: MATH 141
 Restriction(s): Not open to students who are taking or who have taken MATH 254.
 Symbols:
 Terms
 Fall 2019
 Instructors
 Jerome Vetois

MATH 323 Probability 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Sample space, events, conditional probability, independence of events, Bayes' Theorem. Basic combinatorial probability, random variables, discrete and continuous univariate and multivariate distributions. Independence of random variables. Inequalities, weak law of large numbers, central limit theorem.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 141 or equivalent.
 Restriction: Intended for students in Science, Engineering and related disciplines, who have had differential and integral calculus
 Restriction: Not open to students who have taken or are taking MATH 356
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Jose Andres Correa
 David B Wolfson, Djivede A Kelome

MATH 324 Statistics 3 Credits+
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, contingency tables, nonparametric inference, regression, Bayesian inference.
Offered by: Mathematics and Statistics
 Fall and Winter
 Prerequisite: MATH 323 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 357
 You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar.
 Symbols:
 +
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Masoud AsgharianDastenaei

MATH 423 Regression&Anal of Variance 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Leastsquares estimators and their properties. Analysis of variance. Linear models with general covariance. Multivariate normal and chisquared distributions; quadratic forms. General linear hypothesis: Ftest and ttest. Prediction and confidence intervals. Transformations and residual plot. Balanced designs.
Offered by: Mathematics and Statistics
 Fall
 Prerequisites: MATH 324, and MATH 223 or MATH 236
 Restriction: Not open to students who have taken or are taking MATH 533.
 Symbols:
 Terms
 Fall 2019
 Instructors
 Yi Yang
Complementary Courses
18 or 21 credits
03 credits from:

MATH 203 Principles of Statistics 1 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Examples of statistical data and the use of graphical means to summarize the data. Basic distributions arising in the natural and behavioural sciences. The logical meaning of a test of significance and a confidence interval. Tests of significance and confidence intervals in the one and two sample setting (means, variances and proportions).
Offered by: Mathematics and Statistics
 No calculus prerequisites
 Restriction: This course is intended for students in all disciplines. For extensive course restrictions covering statistics courses see Section 3.6.1 of the Arts and of the Science sections of the calendar regarding course overlaps.
 You may not be able to receive credit for this course and other statistic courses. Be sure to check the Course Overlap section under Faculty Degree Requirements in the Arts or Science section of the Calendar. Students should consult http://www.mcgill.ca/students/transfercredit for information regarding transfer credits for this course.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 David B Wolfson, Abbas Khalili Mahmoudabadi
 Yi Yang
At least 6 credits selected from:
* Students can take either MATH 317 or COMP 350, but not both.

COMP 250 Intro to Computer Science 3 Credits
 Fall
 Winter
 Summer
Offered in the:Computer Science (Sci): Mathematical tools (binary numbers, induction, recurrence relations, asymptotic complexity, establishing correctness of programs), Data structures (arrays, stacks, queues, linked lists, trees, binary trees, binary search trees, heaps, hash tables), Recursive and nonrecursive algorithms (searching and sorting, tree and graph traversal). Abstract data types, inheritance. Selected topics.
Offered by: Computer Science
 3 hours
 Prerequisites: Familiarity with a high level programming language and CEGEP level Math.
 Students with limited programming experience should take COMP 202 or equivalent before COMP 250. See COMP 202 Course Description for a list of topics.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Michael Langer, Giulia Alberini
 Reihaneh Rabbany, Giulia Alberini

COMP 350 Numerical Computing 3 Credits*
 Fall
 Winter
 Summer
Offered in the:Computer Science (Sci): Computer representation of numbers, IEEE Standard for Floating Point Representation, computer arithmetic and rounding errors. Numerical stability. Matrix computations and software systems. Polynomial interpolation. Leastsquares approximation. Iterative methods for solving a nonlinear equation. Discretization methods for integration and differential equations.
Offered by: Computer Science
 3 hours
 Prerequisites: MATH 222 and MATH 223 and one of: COMP 202, COMP 208, COMP 250; or equivalents.
 Restrictions: Students cannot receive credit for both COMP 350 and MATH 317.
 Symbols:
 *
 Terms
 Fall 2019
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 243 Analysis 2 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Definition and properties of Riemann integral, Fundamental Theorem of Calculus, Taylor's theorem. Infinite series: alternating, telescoping series, rearrangements, conditional and absolute convergence, convergence tests. Power series and Taylor series. Elementary functions. Introduction to metric spaces.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 Winter 2020
 Instructors
 Axel W Hundemer

MATH 314 Advanced Calculus 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Derivative as a matrix. Chain rule. Implicit functions. Constrained maxima and minima. Jacobians. Multiple integration. Line and surface integrals. Theorems of Green, Stokes and Gauss. Fourier series with applications.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 133, MATH 222
 Restriction: Not open to students who have taken or are taking MATH 248 or MATH 358.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Charles Roth

MATH 315 Ordinary Differential Eqns 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): First order ordinary differential equations including elementary numerical methods. Linear differential equations. Laplace transforms. Series solutions.
Offered by: Mathematics and Statistics
 Prerequisite: MATH 222.
 Corequisite: MATH 133.
 Restriction: Not open to students who have taken or are taking MATH 325.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Rosalie BélangerRioux

MATH 316 Complex Variables 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Algebra of complex numbers, CauchyRiemann equations, complex integral, Cauchy's theorems. Taylor and Laurent series, residue theory and applications.
Offered by: Mathematics and Statistics
 Fall
 Prerequisites: MATH 314 or equivalent and MATH 243.
 Restriction: Not open to students who have taken or are taking MATH 249, MATH 366, MATH 381 or MATH 466.
 Symbols:
 Terms
 Fall 2019
 Instructors
 Brent Pym

MATH 317 Numerical Analysis 3 Credits*
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Error analysis. Numerical solutions of equations by iteration. Interpolation. Numerical differentiation and integration. Introduction to numerical solutions of differential equations.
Offered by: Mathematics and Statistics
 Fall
 Prerequisites: MATH 315 or MATH 325 or MATH 263, and COMP 202 or permission of instructor.
 Restrictions: Not open to students who have taken COMP 350
 Symbols:
 *
 Terms
 Fall 2019
 Instructors
 Peter Bartello

MATH 326 Nonlinear Dynamics and Chaos 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Linear systems of differential equations, linear stability theory. Nonlinear systems: existence and uniqueness, numerical methods, one and two dimensional flows, phase space, limit cycles, PoincareBendixson theorem, bifurcations, Hopf bifurcation, the Lorenz equations and chaos.
Offered by: Mathematics and Statistics
 Fall
 Prerequisites: MATH 222, MATH 223
 Restriction: Not open to students who have taken or are taking MATH 376
 Symbols:
 Terms
 Fall 2019
 Instructors
 Antony Raymond Humphries

MATH 327 Matrix Numerical Analysis 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): An overview of numerical methods for linear algebra applications and their analysis. Problem classes include linear systems, least squares problems and eigenvalue problems.
Offered by: Mathematics and Statistics
 Winter
 Prerequisites: MATH 223 or MATH 236 or MATH 247 or MATH 251, COMP 202 or consent of instructor.
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 329 Theory of Interest 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Simple and compound interest, annuities certain, amortization schedules, bonds, depreciation.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 141
 Symbols:
 Terms
 Winter 2020
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 340 Discrete Mathematics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Discrete Mathematics and applications. Graph Theory: matchings, planarity, and colouring. Discrete probability. Combinatorics: enumeration, combinatorial techniques and proofs.
Offered by: Mathematics and Statistics
 Winter
 Prerequisites: MATH 235 or MATH 240 or MATH 242.
 Corequisites: MATH 223 or MATH 236.
 Restriction: Restriction: Not open to students who have taken or are taking MATH 350.
 Restriction: Not open to students who have taken or are taking MATH 343 or MATH 350.
 Symbols:
 Terms
 Winter 2020
 Instructors
 Jérôme Fortier

MATH 350 Honours Discrete Mathematics 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Discrete mathematics. Graph Theory: matching theory, connectivity, planarity, and colouring; graph minors and extremal graph theory. Combinatorics: combinatorial methods, enumerative and algebraic combinatorics, discrete probability.
Offered by: Mathematics and Statistics
 Prerequisites: MATH 235 or MATH 240 and MATH 251 or MATH 223.
 Restrictions: Not open to students who have taken or are taking MATH 340. Intended for students in mathematics or computer science honours programs.
 Intended for students in mathematics or computer science honours programs.
 Symbols:
 Terms
 Fall 2019
 Instructors
 Sergey Norin

MATH 417 Linear Optimization 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): An introduction to linear optimization and its applications: Duality theory, fundamental theorem, sensitivity analysis, convexity, simplex algorithm, interiorpoint methods, quadratic optimization, applications in game theory.
Offered by: Mathematics and Statistics
 Prerequisites: COMP 202, and MATH 223 or MATH 236, and MATH 314 or equivalent
 Restriction: Not open to students who have taken or are taking MATH 487 or MATH 517.
 Symbols:
 Terms
 Fall 2019
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 430 Mathematical Finance 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Introduction to concepts of price and hedge derivative securities. The following concepts will be studied in both concrete and continuous time: filtrations, martingales, the change of measure technique, hedging, pricing, absence of arbitrage opportunities and the Fundamental Theorem of Asset Pricing.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 Winter 2020
 Instructors
 Djivede A Kelome
At least 9 credits selected from:
*Students can take either MATH 410 or MATH 420, but not both.

CCOM 314 Communicating Science 3 Credits
 Fall
 Winter
 Summer
Offered in the:Communication (SCS): Production of written and oral assignments designed to communicate scientific problems and findings to varied audiences. Analysis of the disciplinary conventions of scientific discourse in terms of audience, purpose, organization, and style; comparative rhetorical analysis of academic and popular genres, including abstracts, lab reports, research papers, print and online journalism.
Offered by: McGill Writing Centre
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Diane Y Dechief
 Diane Y Dechief

COMP 551 Applied Machine Learning 4 Credits
 Fall
 Winter
 Summer
Offered in the:Computer Science (Sci): Selected topics in machine learning and data mining, including clustering, neural networks, support vector machines, decision trees. Methods include feature selection and dimensionality reduction, error estimation and empirical validation, algorithm design and parallelization, and handling of large data sets. Emphasis on good methods and practices for deployment of real systems.
Offered by: Computer Science
 Prerequisite(s): MATH 323 or ECSE 205 or ECSE 305 or equivalent
 Restriction(s): Not open to students who have taken COMP 598 when topic was "Applied Machine Learning"
 Some background in Artificial Intelligence is recommended, e.g. COMP424 or ECSE526, but not required.
 Symbols:
 Terms
 Fall 2019
 Winter 2020
 Instructors
 William L Hamilton

MATH 208 Intro to Statistical Computing 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Basic data management. Data visualization. Exploratory data analysis and descriptive statictics. Writing functions. Simulation and parallel computing. Communication data and documenting code for reproducible research.
Offered by: Mathematics and Statistics
 Prerequisite(s): MATH 133
 Symbols:
 Terms
 Fall 2019
 Instructors
 Russell Steele

MATH 410 Majors Project 3 Credits*
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): A supervised project.
Offered by: Mathematics and Statistics
 Prerequisite: Students must have 21 completed credits of the required mathematics courses in their program, including all required 200 level mathematics courses.
 Requires departmental approval.
 Symbols:
 *
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Djivede A Kelome, Russell Steele
 Djivede A Kelome

MATH 420 Independent Study 3 Credits*
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Reading projects permitting independent study under the guidance of a staff member specializing in a subject where no appropriate course is available. Arrangements must be made with an instructor and the Chair before registration.
Offered by: Mathematics and Statistics
 Fall and Winter and Summer
 Requires approval by the chair before registration
 Please see regulations concerning Project Courses under Faculty Degree Requirements
 Symbols:
 *
 Terms
 Fall 2019
 Winter 2020
 Instructors
 Johanna Neslehova, Marcin Sabok
 Johanna Neslehova

MATH 427 Statistical Quality Control 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Introduction to quality management; variability and productivity. Quality measurement: capability analysis, gauge capability studies. Process control: control charts for variables and attributes. Process improvement: factorial designs, fractional replications, response surface methodology, Taguchi methods. Acceptance sampling: operating characteristic curves; single, multiple and sequential acceptance sampling plans for variables and attributes.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 Fall 2019
 Instructors
 Christian Genest

MATH 447 Intro. to Stochastic Processes 3 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Conditional probability and conditional expectation, generating functions. Branching processes and random walk. Markov chains, transition matrices, classification of states, ergodic theorem, examples. Birth and death processes, queueing theory.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 323
 Restriction: Not open to students who have taken or are taking MATH 547.
 Symbols:
 Terms
 Winter 2020
 Instructors
 Russell Steele

MATH 523 Generalized Linear Models 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Modern discrete data analysis. Exponential families, orthogonality, link functions. Inference and model selection using analysis of deviance. Shrinkage (Bayesian, frequentist viewpoints). Smoothing. Residuals. Quasilikelihood. Contingency tables: logistic regression, loglinear models. Censored data. Applications to current problems in medicine, biological and physical sciences. R software.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 Winter 2020
 Instructors
 Johanna Neslehova

MATH 524 Nonparametric Statistics 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Distribution free procedures for 2sample problem: Wilcoxon rank sum, SiegelTukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: KruskalWallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chisquare, likelihood ratio, KolmogorovSmirnov tests. Statistical software packages used.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 525 Sampling Theory & Applications 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Simple random sampling, domains, ratio and regression estimators, superpopulation models, stratified sampling, optimal stratification, cluster sampling, sampling with unequal probabilities, multistage sampling, complex surveys, nonresponse.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 540 Life Actuarial Mathematics 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Life tables and distributions; force of mortality; premium, net premium, and reserve valuation for life insurance and annuity contracts (discrete and continuous case); cash flow analysis for portfolios of life insurance and annuities; asset liability management; numerical techniques for multiple decrement and state models; portfolio valuation of aggregate risks.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 541 Nonlife Actuarial Models 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Stochastic models and inference for loss severity and claim frequency distributions; computational techniques for the aggregation of independent risks (Panjer's algorithm, FFT, etc.); risk measures and quantitative risk management applications; models and inference for multivariate data, heavytail distributions, and extremes; dynamic risk models based on stochastic processes and ruin theory.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 This course is not scheduled for the 20192020 academic year
 Instructors
 There are no professors associated with this course for the 20192020 academic year

MATH 545 Intro to Time Series Analysis 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Stationary processes; estimation and forecasting of ARMA models; nonstationary and seasonal models; statespace models; financial time series models; multivariate time series models; introduction to spectral analysis; long memory models.
Offered by: Mathematics and Statistics
 Symbols:
 Terms
 Winter 2020
 Instructors
 Russell Steele

MATH 556 Mathematical Statistics 1 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Distribution theory, stochastic models and multivariate transformations. Families of distributions including locationscale families, exponential families, convolution families, exponential dispersion models and hierarchical models. Concentration inequalities. Characteristic functions. Convergence in probability, almost surely, in Lp and in distribution. Laws of large numbers and Central Limit Theorem. Stochastic simulation.
Offered by: Mathematics and Statistics
 Fall
 Prerequisite: MATH 357 or equivalent
 Symbols:
 Terms
 Fall 2019
 Instructors
 David A Stephens

MATH 557 Mathematical Statistics 2 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): Sampling theory (including largesample theory). Likelihood functions and information matrices. Hypothesis testing, estimation theory. Regression and correlation theory.
Offered by: Mathematics and Statistics
 Winter
 Prerequisite: MATH 556
 Symbols:
 Terms
 Winter 2020
 Instructors
 Masoud AsgharianDastenaei

MATH 598 Topics in Probability & Stats 4 Credits
 Fall
 Winter
 Summer
Offered in the:Mathematics & Statistics (Sci): This course covers a topic in probability and/or statistics.
Offered by: Mathematics and Statistics
 Prerequisite(s): At least 30 credits in required or complementary courses from the Honours in Probability and Statistics program including MATH 356. Additional prerequisites may be imposed by the Department of Mathematics and Statistics depending on the nature of the topic.
 Restriction(s): Requires permission of the Department of Mathematics and Statistics.
 Symbols:
 Terms
 Winter 2020
 Instructors
 Jessica Lin